Predictive Optimal Iterative Learning Control for Nonlinear Systems Using the Koopman Operator

This paper develops a predictive optimal iterative learning control design for nonlinear systems based on the Koopman operator. Iterative learning control applies to systems that undergo repeated executions, known as trials, over a finite duration, the trial length. Once a trial is complete, all information generated is available to update the control signal for the subsequent trial. The first step in design is to approximately model the nonlinear system as a high‐dimensional linear model using the Koopman operator and extended dynamic mode decomposition, which is applied on each trial. Then, an iterative learning control law is designed with predictive action over an infinite duration in the trial‐to‐trial direction. The robust convergence of the tracking error is analyzed, and a numerical case study demonstrates the effectiveness of the design.